Transmission line system



March 14, 1939. w,.vAN B, ROBERT 2,150,24

TRANSMISSION LINE SYSTEM Filed Sept. s, 1937 72 b fib Z'RANSM/ TTEI? R mE O M 0 m v v v 05 9 8 w/ J 3 J 1 0 a 7 lloo L mm E n M A my 2/ T B N Ro 0 M m A Of 0 0 0 0 0 w ,0, u m m 3% 3 wuzfiuwwk Y WEE "AN 5'. ROBERTSB A TTORNEY.

Patented Mar. 14, 1939 UNITED STATES 2,150,246 TRANSDIISSION LINE SYSTEMWalter van B. Roberts, Princeton, N. J., assignor to Radio Corporationof America, a corporation of Delaware Application September 3, 1937,Serial No. 162,302

9 Claims.

This invention relates to transmission line systems, particularly toradio frequency transmission systems, and has for its primary object totransform in a simple and inexpensive manner the value of a load orterminating impedance, such as an antenna, to a pure resistance of avalue equal to the characteristic impedance of the associated line.

In order to avoid reflection losses in high frequency systems, atransmission line should be terminated by a pure resistance equal to thecharacteristic or surge impedance of the line. In practice, however, itis found that the load to be fed by the line is often not a pureresistance. It is well known, however, that the load may be madeeffectively a pure resistance by connecting suitable reactance elementsin series or shunt to it. It is also known that a suitable length oftransmission line, either open or shorted at its far end, may beconnected across the load to function as a suitable reactance for thepurpose of neutralizing the reactance component of the load.

Fig. 1 is given for the purpose of exposition, and

illustrates avknown transmission line system;

Fig. 2 illustrates a simple embodiment of the present invention; and

Fig. 3 illustrates a graphical method for determining the constants ofthe structure employed in thepresent invention.

In Fig. 1 there is shown a load Z, such as an antenna, fed by atransmission line TL. An extra section of transmission line T1L1 isprovided across the load to transform the load Z to a pure 5 resistance.

The efiect of the extra section of line T1L1 is to make the load aneffective resistance which, however, in general differs in value fromthe characteristic or surge impedance of the main transmission line TLfeeding it. There is therefore'inserted, in accordance with knownprinciples, a' matching section I comprising two spaced conductors whoselength is one-quarter the length of the communication wave and whosecharacteristic impedance is the geometric mean between the eifectiveload resistance and the characteristic impedance of the main line. The

. impedance of this quarter Wave matching section I is determined by thegeometry of the section,

in well known manner.

One disadvantage of the arrangement of Fig. 1 is that there must beprovided an extra length of line, suchas T1L1. whose sole purpose is tomake the load efiectively a pureresistance.

In accordance with the present invention, the

foregoing disadvantage is overcome and the extra section of linedispensed with by inserting the quarter wave matching. section I notbetween the main line TL and the load, as shown in Fig.

1, but at a particular point in the main line itself, 5 note Fig. 2. Inthis way no greater total length of transmission line is required thanthe minimum necessary to reach from the source to the load.

Fig. 2 illustrates the present invention as ap- 1Q plied to a simpletransmission line system comprising a transmitter T feeding highfrequency energy to a load Z overa main transmission line TL. Inaccordance with the present invention a quarter wave-length section ofline I having 15 terminals 0., a and b, b is inserted in the main lineat a particular location between the load Z and the transmitter T, andat an electrical distance 0 which is preferably less than one-quarterthe length of the communication wave. 20

The length of the section 0 between the matching section I and the loadZ may be determined by a simple graphical method which is illustrated ina particular case in Fig. 3.

In Fig. 3 it is assumed that the impedance of 25 the load Z and thecharacteristic impedance p or" the line 2 are known, and that Z has avalue of 320-14240, while p is 300. When the points Z and Z+5i in thecomplex plane may be plotted and connected by a straight line, in themanner 30 shown in Fig. 3 by the vertical line V, the lower end of saidline'V being Z and the upper end being Z+i Let us now subdivide thisvertical V line into equal portions, for example ten portions, andnumber the division points on the line 35 uniformly so that the bottomof the line bears the number zero and the top of the line bears thenumber 1, as illustrated.

Let us next draw a line joining the points p and +7Z and similarlysubdivide into equal por- 40 tions and number in the manner shown inFig.

3 by the slanted line S. Let us furtherlay off a straight line M fromthe origin 0 of the complex plane, such that it cuts the two scales ofnumbers V and S at the same Value. This value 45 is tan 0, so theelectrical length of the line 0 is thus determined which will make theimpedance measured at terminals a, a looking toward necessary wheneverthe required electrical length exceeds 45.

The impedance measured at terminals a, a when 0 is given the valuedetermined, as explained above, is a pure resistance equal to thecharacteristic impedance of the line 2 (between a, a and Z) multipliedby the ratio of the distance from the origin 0 to the intersection oflines V and M, to the distance from the origin 0 to the mtersection oflines S and M. In Fig. 3 this is 300 is a real quantity, and fordetermining the value of said expression when 0 is so chosen. Z is thecomplex load impedance and p the characteristic impedance of the line 2.

It should be noted that it is not necessary to make the line section 2,which is adjacent the load Z, of the same characteristic impedance asthe main line TL. In practice, the impedance of the section 2 adjacentthe load and the impedance of the load itself, if possible, will beadjusted by mathematical cut and try, in accordance with the methodexplained above, so as to obtain the ost convenient spacings betweenconductors for the quarter wave section I and the section 2 adjacent theload.

It should be understood that the matching line section I can be aquarter wavelength or any odd multiple thereof, and the section 2, whilepreferably less than oneequarter wavelength, may be increased by anymultiple of a half wavelength without affecting the principles involved.

What is claimed is:

1. The method of preventing wave reflection in a transmission lineconnecting a source of high frequency energy to a complex load impedancewhich comprises changing the spacing of said line for a distance equalto an odd multiple including unity of a quarter wavelength at a position in said line which is removed from said load by a length so chosenas to make the effective impedance of said load and said length of linea pure resistance, and further so choosing the constants of said changedsection of line as to make its characteristic impedance equal to thegeometric mean between said resistance and the characteristic impedanceof the line located between said source and changed section whereby saidpure resistance is transformed to a value equal to the line impedance.

2. Themethod of preventing wave reflection in a transmission lineconnecting a source of high frequency energy to a complex load impedancewhich comprises changing the spacing of said line for a distance equalto an odd multiple including unity of a quarter wavelength at a positionin said line which is removed from said load by a length equal to anintegral number of half wave lengths plus an additional length greaterthan zero and less than a quarter wave length, said additional lengthbeing so chosen as to make the effective impedance of said load and saidlength of line a pure resistance, and further so choosing the constantsof said changed section of line as to make its characteristic impedanceequal to the geometric mean between said resistance and thecharacteristic impedance of the line located between said source andchanged section, whereby said pure resistance is transformed to a valueequal to the line impedance.

3. In combination in a high frequency system, a complex load impedanceZ, a section of transmission line terminated thereby and having anelectrical length 0 so chosen as to make the input impedance of saidsection of line expressed by the term Z+j tan 0 p+jZ tan 6 a realquantity, where p is the characteristic impedance of said line, wherebythe input impedance of said section of line is a pure resistance.

4. In combination in a high frequency system, a complex load impedanceZ, a section of transmission line terminated thereby and having anelectrical length 0 so chosen as to make the input impedance of saidsction of line expressed by the term Z+jp tan 6 p+jZ t 0 a realquantity, where p is the characteristic impedance of said line, wherebythe input impedance of said section of line is a pure resistance, asource of high frequency energy including a main transmission linecoupled to said section of line, and means between said maintransmission line and said section of line for matching the resistanceof said source to the input impedance of said section of line.

5. In combination in a high frequency system, a complex load impedanceZ, a section of transmission line terminated thereby and having anelectrical length 0 so chosen as to make the input impedance of saidsection of line expressed by the term Z+j tan 8 +jZ tan 0 a realquantity, where p is the characteristic impedance of said line, wherebythe input impedance of said section of line is a pure resistance, saidelectrical length 0 being less than one-quarter wavelength long.

6. In combination in a high frequency system, a complex load impedanceZ, a section of transmission line terminated thereby and having anelectrical length 6 so chosen as to make the input impedance of saidsection of line expressed by the term a real quantity, where p is thecharacteristic impedance of said line, whereby the input impedance ofsaid section of line is a pureresistance, said electrical length being aquantity less than one-quarter wavelength long plus a multiple ofone-half wavelength, 7

'7. In a high frequency system,a complex load impedance, a 'firstsection of' line having one terminal coupled to said lead, a secondsection of line a'quarter wavelength long or an odd multiple thereof, asource of energy coupled to one terminal of said second section of line,the other terminal of said second section of line being coupled to theother terminal of said first section of line, said first'se ction ofline having such an electrical length asto make the effective impedanceof said load and said first section of line a pure resistance, saidsecond section of line having a characteristic impedance which is thegeometric mean between said pure resistance and the impedance of saidsource, whereby said pure resistance is transformed to a value equal tothe line impedance.

8. A system in accordance with claim 7,inc1uding a third section of lineconnected between said source and said second section, said thirdsection of line having the same geometrical structure as said firstsection.

9. A system in accordance with claim '7, including a third section ofline connected between said source and said second section, said thirdsection of line having a different geometrical structure than said firstsection.

WALTER VAN B. ROBERTS.

